Average Error: 5.8 → 2.1
Time: 15.9s
Precision: 64
\[2.0 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\]
↓
\[2.0 \cdot \left(\left(y \cdot x + z \cdot t\right) - \sqrt[3]{\left(a + b \cdot c\right) \cdot \left(c \cdot i\right)} \cdot \left(\sqrt[3]{\left(a + b \cdot c\right) \cdot \left(c \cdot i\right)} \cdot \left(\sqrt[3]{c \cdot i} \cdot \sqrt[3]{a + b \cdot c}\right)\right)\right)\]
2.0 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)
↓
2.0 \cdot \left(\left(y \cdot x + z \cdot t\right) - \sqrt[3]{\left(a + b \cdot c\right) \cdot \left(c \cdot i\right)} \cdot \left(\sqrt[3]{\left(a + b \cdot c\right) \cdot \left(c \cdot i\right)} \cdot \left(\sqrt[3]{c \cdot i} \cdot \sqrt[3]{a + b \cdot c}\right)\right)\right)
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r13901005 = 2.0;
        double r13901006 = x;
        double r13901007 = y;
        double r13901008 = r13901006 * r13901007;
        double r13901009 = z;
        double r13901010 = t;
        double r13901011 = r13901009 * r13901010;
        double r13901012 = r13901008 + r13901011;
        double r13901013 = a;
        double r13901014 = b;
        double r13901015 = c;
        double r13901016 = r13901014 * r13901015;
        double r13901017 = r13901013 + r13901016;
        double r13901018 = r13901017 * r13901015;
        double r13901019 = i;
        double r13901020 = r13901018 * r13901019;
        double r13901021 = r13901012 - r13901020;
        double r13901022 = r13901005 * r13901021;
        return r13901022;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r13901023 = 2.0;
        double r13901024 = y;
        double r13901025 = x;
        double r13901026 = r13901024 * r13901025;
        double r13901027 = z;
        double r13901028 = t;
        double r13901029 = r13901027 * r13901028;
        double r13901030 = r13901026 + r13901029;
        double r13901031 = a;
        double r13901032 = b;
        double r13901033 = c;
        double r13901034 = r13901032 * r13901033;
        double r13901035 = r13901031 + r13901034;
        double r13901036 = i;
        double r13901037 = r13901033 * r13901036;
        double r13901038 = r13901035 * r13901037;
        double r13901039 = cbrt(r13901038);
        double r13901040 = cbrt(r13901037);
        double r13901041 = cbrt(r13901035);
        double r13901042 = r13901040 * r13901041;
        double r13901043 = r13901039 * r13901042;
        double r13901044 = r13901039 * r13901043;
        double r13901045 = r13901030 - r13901044;
        double r13901046 = r13901023 * r13901045;
        return r13901046;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Bits error versus b

Bits error versus c

Bits error versus i

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original5.8
Target1.8
Herbie2.1
\[2.0 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right)\]

Derivation

  1. Initial program 5.8

    \[2.0 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\]
  2. Using strategy rm

  3. Applied associate-*l*1.8

    \[\leadsto 2.0 \cdot \left(\left(x \cdot y + z \cdot t\right) - \color{blue}{\left(a + b \cdot c\right) \cdot \left(c \cdot i\right)}\right)\]
  4. Using strategy rm

  5. Applied add-cube-cbrt2.2

    \[\leadsto 2.0 \cdot \left(\left(x \cdot y + z \cdot t\right) - \color{blue}{\left(\sqrt[3]{\left(a + b \cdot c\right) \cdot \left(c \cdot i\right)} \cdot \sqrt[3]{\left(a + b \cdot c\right) \cdot \left(c \cdot i\right)}\right) \cdot \sqrt[3]{\left(a + b \cdot c\right) \cdot \left(c \cdot i\right)}}\right)\]
  6. Using strategy rm

  7. Applied cbrt-prod2.1

    \[\leadsto 2.0 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\sqrt[3]{\left(a + b \cdot c\right) \cdot \left(c \cdot i\right)} \cdot \color{blue}{\left(\sqrt[3]{a + b \cdot c} \cdot \sqrt[3]{c \cdot i}\right)}\right) \cdot \sqrt[3]{\left(a + b \cdot c\right) \cdot \left(c \cdot i\right)}\right)\]

  8. Final simplification2.1

    \[\leadsto 2.0 \cdot \left(\left(y \cdot x + z \cdot t\right) - \sqrt[3]{\left(a + b \cdot c\right) \cdot \left(c \cdot i\right)} \cdot \left(\sqrt[3]{\left(a + b \cdot c\right) \cdot \left(c \cdot i\right)} \cdot \left(\sqrt[3]{c \cdot i} \cdot \sqrt[3]{a + b \cdot c}\right)\right)\right)\]

Reproduce

herbie shell --seed 2019156 
(FPCore (x y z t a b c i)
  :name "Diagrams.ThreeD.Shapes:frustum from diagrams-lib-1.3.0.3, A"

  :herbie-target
  (* 2.0 (- (+ (* x y) (* z t)) (* (+ a (* b c)) (* c i))))

  (* 2.0 (- (+ (* x y) (* z t)) (* (* (+ a (* b c)) c) i))))